Blocks of the category of cuspidal $\mathfrak{sp}_{2n}$-modules

TL;DR

This paper establishes an equivalence between blocks of cuspidal generalized weight modules over sp(2n) and modules over a formal power series ring, providing a new structural understanding of these modules.

Contribution

It proves that each block of cuspidal generalized weight modules over sp(2n) is equivalent to modules over a formal power series ring, revealing their algebraic structure.

Findings

Blocks are equivalent to modules over C[[t_1,...,t_n]]

Provides a classification framework for cuspidal modules

Enhances understanding of module categories over sp(2n)

Abstract

We show that every block of the category of cuspidal generalized weight modules with finite dimensional generalized weight spaces over the Lie algebra sp(2n)(C) is equivalent to the category of finite dimensional C[[t_1,t_2,...,t_n]]-modules.